%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP660+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:35:03 PM UTC 2026
% Result : Theorem 61.11s 8.64s
% Output : CNFRefutation 61.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 6
% Syntax : Number of formulae : 164 ( 155 unt; 0 def)
% Number of atoms : 173 ( 172 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 18 ~; 7 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 308 ( 302 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [C,B,A] : mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [X0,X1] :
( mult(ld(X1,X1),X0) = X0
& mult(X0,ld(X1,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( mult(ld(X1,X1),X0) = X0
& mult(X0,ld(X1,X1)) = X0 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),X2),X0) = mult(X0,mult(X1,mult(X2,X0))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
? [X0,X1] :
( mult(ld(X1,X1),X0) != X0
| mult(X0,ld(X1,X1)) != X0 ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f14,plain,
( ? [X0,X1] : mult(ld(X1,X1),X0) != X0
| ? [X0,X1] : mult(X0,ld(X1,X1)) != X0 ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
( mult(ld(sK3_skl,sK3_skl),sK2_skl) != sK2_skl
| mult(sK0_skl,ld(sK1_skl,sK1_skl)) != sK0_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X1,sK3_skl)],[f14]) ).
fof(f16,plain,
( mult(ld(sK3_skl,sK3_skl),sK2_skl) != sK2_skl
| mult(sK0_skl,ld(sK1_skl,sK1_skl)) != sK0_skl ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
! [X0,X1,X2] : mult(mult(X0,mult(X1,mult(X2,X0))),mult(X0,X1)) = mult(mult(X0,X1),mult(X2,mult(X0,mult(X0,X1)))),
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f22,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(X2,mult(ld(X2,X0),mult(X1,X2))),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f23,plain,
! [X0,X1,X2] : ld(mult(mult(X0,X1),X2),mult(X0,mult(X1,mult(X2,X0)))) = X0,
inference(paramodulation,[status(thm)],[f12,f9]) ).
fof(f32,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),mult(X2,mult(X0,mult(X0,X1)))),X0) = mult(X0,mult(mult(X1,mult(X2,X0)),mult(mult(X0,X1),X0))),
inference(paramodulation,[status(thm)],[f19,f12]) ).
fof(f43,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(mult(X2,mult(X0,mult(X0,X1))),X0))) = mult(X0,mult(mult(X1,mult(X2,X0)),mult(mult(X0,X1),X0))),
inference(forward_demodulation,[status(thm)],[f12,f32]) ).
fof(f51,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),mult(mult(X2,X0),X1)),mult(mult(X0,X1),X1)) = mult(mult(mult(X0,X1),X1),mult(ld(X1,X2),mult(mult(X0,X1),mult(mult(X0,X1),X1)))),
inference(paramodulation,[status(thm)],[f22,f19]) ).
fof(f55,plain,
! [X0,X1,X2] : ld(X0,mult(mult(X1,X2),X0)) = mult(ld(X0,X1),mult(X2,X0)),
inference(paramodulation,[status(thm)],[f22,f9]) ).
fof(f87,plain,
! [X0,X1] : mult(X0,X1) = mult(ld(mult(X0,X1),X0),mult(X1,mult(X0,X1))),
inference(paramodulation,[status(thm)],[f9,f55]) ).
fof(f95,plain,
! [X0,X1,X2] : ld(X0,mult(X1,X0)) = mult(ld(X0,X2),mult(ld(X2,X1),X0)),
inference(paramodulation,[status(thm)],[f8,f55]) ).
fof(f124,plain,
! [X0,X1] : ld(ld(mult(X0,X1),X0),mult(X0,X1)) = mult(X1,mult(X0,X1)),
inference(paramodulation,[status(thm)],[f87,f9]) ).
fof(f167,plain,
! [X0,X1,X2] : ld(X0,mult(X1,X0)) = mult(X2,mult(ld(mult(X0,X2),X1),X0)),
inference(paramodulation,[status(thm)],[f9,f95]) ).
fof(f218,plain,
! [X0,X1] : ld(ld(X0,X1),mult(X1,ld(X1,X0))) = mult(ld(X1,X0),mult(X1,ld(X1,X0))),
inference(paramodulation,[status(thm)],[f8,f124]) ).
fof(f239,plain,
! [X0,X1] : ld(ld(X0,X1),X0) = mult(ld(X1,X0),mult(X1,ld(X1,X0))),
inference(forward_demodulation,[status(thm)],[f8,f218]) ).
fof(f246,plain,
! [X0,X1] : ld(ld(X0,X1),X0) = mult(ld(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f8,f239]) ).
fof(f263,plain,
! [X0,X1] : ld(X0,X1) = mult(ld(mult(X1,X0),X1),X1),
inference(paramodulation,[status(thm)],[f9,f246]) ).
fof(f688,plain,
! [X0,X1,X2] : ld(mult(mult(X0,rd(X1,mult(X2,X0))),X2),mult(X0,X1)) = X0,
inference(paramodulation,[status(thm)],[f10,f23]) ).
fof(f698,plain,
! [X0,X1,X2] : ld(X0,mult(X1,X0)) = mult(ld(X0,rd(X1,X2)),mult(X2,X0)),
inference(paramodulation,[status(thm)],[f10,f55]) ).
fof(f701,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,X2)),X2) = mult(X2,mult(ld(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f10,f22]) ).
fof(f705,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f10,f9]) ).
fof(f733,plain,
! [X0,X1] : rd(ld(X0,X1),X1) = ld(mult(X1,X0),X1),
inference(paramodulation,[status(thm)],[f263,f11]) ).
fof(f736,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,mult(X2,X0))),X0) = mult(mult(X0,X1),X2),
inference(paramodulation,[status(thm)],[f12,f11]) ).
fof(f740,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f802,plain,
! [X0,X1,X2] : ld(rd(X0,X1),mult(X2,rd(X0,X1))) = mult(X1,mult(ld(X0,X2),rd(X0,X1))),
inference(paramodulation,[status(thm)],[f705,f95]) ).
fof(f808,plain,
! [X0,X1] : rd(X0,mult(ld(X1,X0),X0)) = ld(X0,X1),
inference(paramodulation,[status(thm)],[f246,f740]) ).
fof(f822,plain,
! [X0,X1] : rd(X0,rd(ld(X1,X0),X0)) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f733,f740]) ).
fof(f835,plain,
! [X0,X1] : rd(X0,mult(X1,X0)) = ld(X0,rd(X0,X1)),
inference(paramodulation,[status(thm)],[f705,f808]) ).
fof(f851,plain,
! [X0,X1] : rd(X0,rd(X1,X0)) = mult(X0,rd(X0,X1)),
inference(paramodulation,[status(thm)],[f705,f822]) ).
fof(f982,plain,
! [X0,X1,X2] : ld(X0,ld(X1,mult(X2,X1))) = mult(ld(mult(X1,X0),X2),X1),
inference(paramodulation,[status(thm)],[f167,f9]) ).
fof(f1067,plain,
! [X0,X1,X2] : rd(mult(X0,X1),X0) = mult(mult(X0,rd(X1,mult(X2,X0))),X2),
inference(paramodulation,[status(thm)],[f688,f740]) ).
fof(f1151,plain,
! [X0,X1,X2] : rd(ld(X0,mult(X1,X0)),mult(X2,X0)) = ld(X0,rd(X1,X2)),
inference(paramodulation,[status(thm)],[f698,f11]) ).
fof(f1334,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),X0) = mult(mult(X0,X1),rd(X2,X0)),
inference(paramodulation,[status(thm)],[f10,f736]) ).
fof(f1784,plain,
! [X0,X1,X2] : rd(mult(X0,mult(ld(X0,X1),X2)),X0) = mult(X1,rd(X2,X0)),
inference(paramodulation,[status(thm)],[f701,f11]) ).
fof(f2430,plain,
! [X0,X1,X2] : ld(X0,ld(X1,X2)) = mult(ld(mult(X1,X0),rd(X2,X1)),X1),
inference(paramodulation,[status(thm)],[f10,f982]) ).
fof(f2541,plain,
! [X0,X1,X2] : rd(rd(mult(X0,X1),X0),X2) = mult(X0,rd(X1,mult(X2,X0))),
inference(paramodulation,[status(thm)],[f1067,f11]) ).
fof(f3007,plain,
! [X0,X1] : rd(mult(X0,X1),ld(X1,rd(X0,X0))) = mult(mult(X0,X1),X1),
inference(paramodulation,[status(thm)],[f1151,f822]) ).
fof(f3184,plain,
! [X0,X1,X2] : rd(mult(X0,X1),X0) = mult(X2,rd(ld(ld(X0,X2),X1),X0)),
inference(paramodulation,[status(thm)],[f8,f1784]) ).
fof(f4274,plain,
! [X0,X1,X2] : rd(rd(mult(X0,X1),X0),rd(X2,X0)) = mult(X0,rd(X1,X2)),
inference(paramodulation,[status(thm)],[f10,f2541]) ).
fof(f4579,plain,
! [X0,X1] : rd(X0,ld(ld(X1,X0),rd(X1,X1))) = mult(mult(X1,ld(X1,X0)),ld(X1,X0)),
inference(paramodulation,[status(thm)],[f8,f3007]) ).
fof(f4594,plain,
! [X0,X1] : mult(mult(mult(X0,X1),X1),ld(X1,rd(X0,X0))) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f3007,f10]) ).
fof(f4632,plain,
! [X0,X1] : rd(X0,ld(ld(X1,X0),rd(X1,X1))) = mult(X0,ld(X1,X0)),
inference(forward_demodulation,[status(thm)],[f8,f4579]) ).
fof(f4717,plain,
! [X0,X1,X2] : ld(X0,rd(mult(X1,X2),X1)) = rd(ld(ld(X1,X0),X2),X1),
inference(paramodulation,[status(thm)],[f3184,f9]) ).
fof(f4836,plain,
! [X0,X1,X2] : rd(rd(X0,X1),rd(X2,X1)) = mult(X1,rd(ld(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f8,f4274]) ).
fof(f4950,plain,
! [X0] : ld(X0,rd(X0,X0)) = mult(rd(X0,X0),ld(X0,rd(X0,X0))),
inference(paramodulation,[status(thm)],[f740,f4632]) ).
fof(f4955,plain,
! [X0,X1] : rd(X0,ld(rd(ld(X1,X0),X0),rd(mult(X0,X1),mult(X0,X1)))) = mult(X0,ld(mult(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f733,f4632]) ).
fof(f4972,plain,
! [X0,X1] : ld(mult(X0,ld(X1,X0)),X0) = ld(ld(X1,X0),rd(X1,X1)),
inference(paramodulation,[status(thm)],[f4632,f705]) ).
fof(f4974,plain,
! [X0] : rd(X0,mult(X0,X0)) = mult(rd(X0,X0),ld(X0,rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f835,f4950]) ).
fof(f4975,plain,
! [X0] : rd(X0,mult(X0,X0)) = mult(rd(X0,X0),rd(X0,mult(X0,X0))),
inference(forward_demodulation,[status(thm)],[f835,f4974]) ).
fof(f4986,plain,
! [X0,X1] : rd(X0,ld(rd(ld(X1,X0),X0),rd(mult(X0,X1),mult(X0,X1)))) = mult(X0,rd(ld(X1,X0),X0)),
inference(forward_demodulation,[status(thm)],[f733,f4955]) ).
fof(f5001,plain,
! [X0,X1] : rd(ld(ld(X0,X1),X1),X1) = ld(ld(X0,X1),rd(X0,X0)),
inference(forward_demodulation,[status(thm)],[f733,f4972]) ).
fof(f5260,plain,
! [X0,X1,X2] : ld(X0,rd(X1,X2)) = rd(ld(ld(X2,X0),ld(X2,X1)),X2),
inference(paramodulation,[status(thm)],[f8,f4717]) ).
fof(f5470,plain,
! [X0] : mult(rd(X0,mult(X0,X0)),mult(X0,X0)) = mult(mult(X0,X0),mult(ld(mult(X0,X0),rd(X0,X0)),X0)),
inference(paramodulation,[status(thm)],[f4975,f701]) ).
fof(f5511,plain,
! [X0] : ld(rd(X0,X0),rd(X0,mult(X0,X0))) = rd(X0,mult(X0,X0)),
inference(paramodulation,[status(thm)],[f4975,f9]) ).
fof(f5515,plain,
! [X0] : X0 = mult(mult(X0,X0),mult(ld(mult(X0,X0),rd(X0,X0)),X0)),
inference(forward_demodulation,[status(thm)],[f10,f5470]) ).
fof(f5517,plain,
! [X0] : X0 = mult(mult(X0,X0),ld(X0,ld(X0,X0))),
inference(forward_demodulation,[status(thm)],[f2430,f5515]) ).
fof(f5589,plain,
! [X0] : rd(X0,ld(ld(X0,ld(X0,X0)),rd(mult(X0,X0),mult(X0,X0)))) = mult(mult(mult(X0,X0),ld(X0,ld(X0,X0))),ld(X0,ld(X0,X0))),
inference(paramodulation,[status(thm)],[f5517,f3007]) ).
fof(f5625,plain,
! [X0] : ld(mult(X0,X0),X0) = ld(X0,ld(X0,X0)),
inference(paramodulation,[status(thm)],[f5517,f9]) ).
fof(f5658,plain,
! [X0] : rd(X0,ld(ld(X0,ld(X0,X0)),rd(mult(X0,X0),mult(X0,X0)))) = mult(X0,ld(X0,ld(X0,X0))),
inference(forward_demodulation,[status(thm)],[f5517,f5589]) ).
fof(f5659,plain,
! [X0] : rd(X0,ld(ld(X0,ld(X0,X0)),rd(mult(X0,X0),mult(X0,X0)))) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f8,f5658]) ).
fof(f5737,plain,
! [X0] : rd(X0,ld(rd(ld(X0,X0),X0),rd(mult(X0,X0),mult(X0,X0)))) = ld(X0,X0),
inference(backward_demodulation,[status(thm)],[f5743,f5659]) ).
fof(f5743,plain,
! [X0] : rd(ld(X0,X0),X0) = ld(X0,ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f733,f5625]) ).
fof(f5789,plain,
! [X0] : mult(X0,rd(ld(X0,X0),X0)) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f4986,f5737]) ).
fof(f5792,plain,
! [X0] : rd(rd(X0,X0),rd(X0,X0)) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f4836,f5789]) ).
fof(f7448,plain,
! [X0,X1,X2] : ld(X0,mult(X0,mult(X1,mult(mult(X2,mult(X0,mult(X0,X1))),X0)))) = mult(mult(X1,mult(X2,X0)),mult(mult(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f43,f9]) ).
fof(f7712,plain,
! [X0,X1,X2] : mult(X0,mult(mult(X1,mult(X2,mult(X2,X0))),X2)) = mult(mult(X0,mult(X1,X2)),mult(mult(X2,X0),X2)),
inference(forward_demodulation,[status(thm)],[f9,f7448]) ).
fof(f8510,plain,
! [X0] : ld(ld(X0,X0),rd(X0,X0)) = rd(X0,X0),
inference(paramodulation,[status(thm)],[f5792,f705]) ).
fof(f8511,plain,
! [X0] : mult(ld(X0,X0),rd(X0,X0)) = rd(X0,X0),
inference(paramodulation,[status(thm)],[f5792,f10]) ).
fof(f8531,plain,
! [X0] : rd(ld(ld(X0,X0),X0),X0) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f5001,f8510]) ).
fof(f8532,plain,
! [X0] : rd(mult(ld(X0,X0),X0),X0) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f246,f8531]) ).
fof(f8533,plain,
( mult(rd(sK3_skl,sK3_skl),sK2_skl) != sK2_skl
| mult(sK0_skl,ld(sK1_skl,sK1_skl)) != sK0_skl ),
inference(backward_demodulation,[status(thm)],[f8586,f16]) ).
fof(f8586,plain,
! [X0] : ld(X0,X0) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f11,f8532]) ).
fof(f8587,plain,
! [X0] : mult(rd(X0,X0),rd(X0,X0)) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f8586,f8511]) ).
fof(f8607,plain,
( mult(rd(sK3_skl,sK3_skl),sK2_skl) != sK2_skl
| mult(sK0_skl,rd(sK1_skl,sK1_skl)) != sK0_skl ),
inference(forward_demodulation,[status(thm)],[f8586,f8533]) ).
fof(f8760,plain,
! [X0,X1] : rd(mult(X0,X1),X0) = mult(X0,rd(ld(rd(X0,X0),X1),X0)),
inference(paramodulation,[status(thm)],[f8586,f3184]) ).
fof(f8770,plain,
! [X0] : rd(X0,rd(X0,X0)) = X0,
inference(paramodulation,[status(thm)],[f8586,f740]) ).
fof(f9264,plain,
! [X0] : mult(mult(rd(X0,X0),rd(X0,X0)),ld(rd(X0,X0),rd(rd(X0,X0),rd(X0,X0)))) = mult(rd(X0,X0),rd(X0,X0)),
inference(paramodulation,[status(thm)],[f8587,f4594]) ).
fof(f9272,plain,
! [X0,X1] : rd(ld(rd(X0,X0),mult(X1,rd(X0,X0))),rd(X0,X0)) = ld(rd(X0,X0),rd(X1,rd(X0,X0))),
inference(paramodulation,[status(thm)],[f8587,f1151]) ).
fof(f9285,plain,
! [X0,X1] : rd(mult(rd(X0,X0),mult(X1,rd(X0,X0))),rd(X0,X0)) = mult(mult(rd(X0,X0),X1),rd(X0,X0)),
inference(paramodulation,[status(thm)],[f8587,f736]) ).
fof(f9287,plain,
! [X0,X1] : ld(rd(X0,X0),mult(X1,rd(X0,X0))) = mult(rd(X0,X0),mult(ld(rd(X0,X0),X1),rd(X0,X0))),
inference(paramodulation,[status(thm)],[f8587,f167]) ).
fof(f9298,plain,
! [X0,X1] : mult(mult(X0,rd(X1,X1)),rd(X1,X1)) = mult(rd(X1,X1),mult(ld(rd(X1,X1),X0),rd(X1,X1))),
inference(paramodulation,[status(thm)],[f8587,f22]) ).
fof(f9383,plain,
! [X0] : mult(rd(X0,X0),ld(rd(X0,X0),rd(rd(X0,X0),rd(X0,X0)))) = mult(rd(X0,X0),rd(X0,X0)),
inference(forward_demodulation,[status(thm)],[f8587,f9264]) ).
fof(f9384,plain,
! [X0] : rd(rd(X0,X0),rd(X0,X0)) = mult(rd(X0,X0),rd(X0,X0)),
inference(forward_demodulation,[status(thm)],[f8,f9383]) ).
fof(f9387,plain,
! [X0] : rd(rd(X0,X0),rd(X0,X0)) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f8587,f9384]) ).
fof(f9406,plain,
! [X0,X1] : rd(mult(X0,mult(ld(X0,X1),rd(X0,X0))),rd(X0,X0)) = ld(rd(X0,X0),rd(X1,rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f802,f9272]) ).
fof(f9450,plain,
! [X0,X1] : mult(X0,mult(ld(X0,X1),rd(X0,X0))) = mult(rd(X0,X0),mult(ld(rd(X0,X0),X1),rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f802,f9287]) ).
fof(f9473,plain,
! [X0,X1] : mult(mult(X0,rd(X1,X1)),rd(X1,X1)) = mult(X1,mult(ld(X1,X0),rd(X1,X1))),
inference(forward_demodulation,[status(thm)],[f9450,f9298]) ).
fof(f11443,plain,
! [X0,X1,X2] : ld(mult(X0,X1),rd(X2,X0)) = rd(ld(X1,ld(X0,X2)),X0),
inference(paramodulation,[status(thm)],[f9,f5260]) ).
fof(f11620,plain,
! [X0] : ld(rd(X0,X0),mult(X0,rd(X0,X0))) = mult(rd(X0,mult(X0,X0)),mult(mult(X0,X0),rd(X0,X0))),
inference(paramodulation,[status(thm)],[f5511,f698]) ).
fof(f11660,plain,
! [X0] : mult(X0,mult(ld(X0,X0),rd(X0,X0))) = mult(rd(X0,mult(X0,X0)),mult(mult(X0,X0),rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f802,f11620]) ).
fof(f11661,plain,
! [X0] : mult(X0,mult(rd(X0,X0),rd(X0,X0))) = mult(rd(X0,mult(X0,X0)),mult(mult(X0,X0),rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f8586,f11660]) ).
fof(f11662,plain,
! [X0] : mult(X0,rd(X0,X0)) = mult(rd(X0,mult(X0,X0)),mult(mult(X0,X0),rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f8587,f11661]) ).
fof(f11663,plain,
! [X0] : rd(X0,rd(X0,X0)) = mult(rd(X0,mult(X0,X0)),mult(mult(X0,X0),rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f851,f11662]) ).
fof(f11664,plain,
! [X0] : X0 = mult(rd(X0,mult(X0,X0)),mult(mult(X0,X0),rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f8770,f11663]) ).
fof(f11665,plain,
! [X0] : X0 = mult(rd(X0,mult(X0,X0)),rd(mult(X0,mult(X0,X0)),X0)),
inference(forward_demodulation,[status(thm)],[f1334,f11664]) ).
fof(f11728,plain,
! [X0,X1] : rd(mult(rd(X0,X0),X1),rd(X0,X0)) = mult(rd(X0,X0),rd(ld(rd(X0,X0),X1),rd(X0,X0))),
inference(paramodulation,[status(thm)],[f9387,f8760]) ).
fof(f11816,plain,
! [X0,X1] : rd(mult(rd(X0,X0),X1),rd(X0,X0)) = rd(rd(X1,rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f4836,f11728]) ).
fof(f11819,plain,
! [X0,X1] : rd(rd(mult(X0,rd(X1,X1)),rd(X1,X1)),rd(X1,X1)) = mult(mult(rd(X1,X1),X0),rd(X1,X1)),
inference(backward_demodulation,[status(thm)],[f11824,f9285]) ).
fof(f11824,plain,
! [X0,X1] : rd(mult(rd(X0,X0),X1),rd(X0,X0)) = rd(rd(X1,rd(X0,X0)),rd(X0,X0)),
inference(forward_demodulation,[status(thm)],[f9387,f11816]) ).
fof(f11981,plain,
! [X0,X1] : rd(X0,rd(X1,X1)) = mult(mult(rd(X1,X1),X0),rd(X1,X1)),
inference(forward_demodulation,[status(thm)],[f11,f11819]) ).
fof(f13152,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,rd(X0,X0))) = rd(ld(rd(X0,X0),ld(rd(X0,X0),X1)),rd(X0,X0)),
inference(paramodulation,[status(thm)],[f8587,f11443]) ).
fof(f16499,plain,
! [X0] : ld(rd(X0,mult(X0,X0)),X0) = rd(mult(X0,mult(X0,X0)),X0),
inference(paramodulation,[status(thm)],[f11665,f9]) ).
fof(f16791,plain,
! [X0] : mult(X0,X0) = rd(mult(X0,mult(X0,X0)),X0),
inference(forward_demodulation,[status(thm)],[f705,f16499]) ).
fof(f17910,plain,
! [X0,X1] : rd(rd(X0,rd(X1,X1)),rd(X1,X1)) = mult(rd(X1,X1),mult(ld(rd(X1,X1),rd(X1,X1)),X0)),
inference(paramodulation,[status(thm)],[f701,f11981]) ).
fof(f17916,plain,
! [X0,X1] : rd(rd(ld(rd(rd(X0,X0),rd(X0,X0)),X1),rd(X0,X0)),rd(X0,X0)) = mult(rd(mult(rd(X0,X0),X1),rd(X0,X0)),rd(X0,X0)),
inference(paramodulation,[status(thm)],[f8760,f11981]) ).
fof(f17925,plain,
! [X0,X1] : rd(ld(rd(X0,X0),X1),rd(X0,X0)) = mult(X1,rd(X0,X0)),
inference(paramodulation,[status(thm)],[f8,f11981]) ).
fof(f17933,plain,
! [X0,X1] : mult(mult(mult(rd(X0,X0),rd(X0,X0)),mult(mult(X1,rd(X0,X0)),rd(X0,X0))),mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0))) = mult(mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0)),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(paramodulation,[status(thm)],[f11981,f51]) ).
fof(f17942,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,rd(X0,X0))) = mult(ld(rd(X0,X0),rd(X0,X0)),mult(X1,rd(X0,X0))),
inference(paramodulation,[status(thm)],[f11981,f55]) ).
fof(f17944,plain,
! [X0,X1] : mult(rd(X0,rd(X1,X1)),rd(X1,X1)) = mult(rd(X1,X1),mult(X0,mult(rd(X1,X1),rd(X1,X1)))),
inference(paramodulation,[status(thm)],[f11981,f12]) ).
fof(f18009,plain,
! [X0,X1] : rd(rd(X0,rd(X1,X1)),rd(X1,X1)) = mult(rd(X1,X1),mult(rd(rd(X1,X1),rd(X1,X1)),X0)),
inference(forward_demodulation,[status(thm)],[f8586,f17910]) ).
fof(f18016,plain,
! [X0,X1] : rd(rd(X0,rd(X1,X1)),rd(X1,X1)) = mult(rd(X1,X1),mult(rd(X1,X1),X0)),
inference(forward_demodulation,[status(thm)],[f9387,f18009]) ).
fof(f18029,plain,
! [X0,X1] : rd(rd(ld(rd(X0,X0),X1),rd(X0,X0)),rd(X0,X0)) = mult(rd(mult(rd(X0,X0),X1),rd(X0,X0)),rd(X0,X0)),
inference(forward_demodulation,[status(thm)],[f9387,f17916]) ).
fof(f18030,plain,
! [X0,X1] : rd(rd(ld(rd(X0,X0),X1),rd(X0,X0)),rd(X0,X0)) = mult(rd(X0,X0),X1),
inference(forward_demodulation,[status(thm)],[f10,f18029]) ).
fof(f18035,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,rd(X0,X0))) = mult(ld(rd(X0,X0),X1),rd(X0,X0)),
inference(backward_demodulation,[status(thm)],[f17925,f13152]) ).
fof(f18036,plain,
! [X0,X1] : rd(mult(X0,rd(X1,X1)),rd(X1,X1)) = mult(rd(X1,X1),X0),
inference(backward_demodulation,[status(thm)],[f17925,f18030]) ).
fof(f18055,plain,
! [X0,X1] : mult(mult(rd(X0,X0),mult(mult(X1,rd(X0,X0)),rd(X0,X0))),mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0))) = mult(mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0)),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f8587,f17933]) ).
fof(f18056,plain,
! [X0,X1] : mult(rd(X0,X0),mult(mult(mult(X1,rd(X0,X0)),mult(rd(X0,X0),mult(rd(X0,X0),rd(X0,X0)))),rd(X0,X0))) = mult(mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0)),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f7712,f18055]) ).
fof(f18057,plain,
! [X0,X1] : mult(rd(X0,X0),mult(mult(mult(X1,rd(X0,X0)),rd(rd(rd(X0,X0),rd(X0,X0)),rd(X0,X0))),rd(X0,X0))) = mult(mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0)),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f18016,f18056]) ).
fof(f18058,plain,
! [X0,X1] : mult(rd(X0,X0),mult(rd(X0,X0),mult(ld(rd(X0,X0),mult(X1,rd(X0,X0))),rd(rd(X0,X0),rd(X0,X0))))) = mult(mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0)),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f701,f18057]) ).
fof(f18059,plain,
! [X0,X1] : rd(rd(mult(ld(rd(X0,X0),mult(X1,rd(X0,X0))),rd(rd(X0,X0),rd(X0,X0))),rd(X0,X0)),rd(X0,X0)) = mult(mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0)),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f18016,f18058]) ).
fof(f18060,plain,
! [X0,X1] : rd(rd(mult(mult(X0,mult(ld(X0,X1),rd(X0,X0))),rd(rd(X0,X0),rd(X0,X0))),rd(X0,X0)),rd(X0,X0)) = mult(mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0)),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f802,f18059]) ).
fof(f18061,plain,
! [X0,X1] : rd(rd(mult(mult(X0,mult(ld(X0,X1),rd(X0,X0))),rd(X0,X0)),rd(X0,X0)),rd(X0,X0)) = mult(mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0)),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f9387,f18060]) ).
fof(f18062,plain,
! [X0,X1] : rd(mult(X0,mult(ld(X0,X1),rd(X0,X0))),rd(X0,X0)) = mult(mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0)),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f11,f18061]) ).
fof(f18063,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,rd(X0,X0))) = mult(mult(mult(rd(X0,X0),rd(X0,X0)),rd(X0,X0)),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f9406,f18062]) ).
fof(f18064,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,rd(X0,X0))) = mult(rd(rd(X0,X0),rd(X0,X0)),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f11981,f18063]) ).
fof(f18065,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,rd(X0,X0))) = mult(rd(X0,X0),mult(ld(rd(X0,X0),X1),mult(mult(rd(X0,X0),rd(X0,X0)),rd(rd(X0,X0),rd(X0,X0))))),
inference(forward_demodulation,[status(thm)],[f9387,f18064]) ).
fof(f18066,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,rd(X0,X0))) = mult(rd(X0,X0),mult(ld(rd(X0,X0),X1),rd(mult(rd(X0,X0),mult(rd(X0,X0),rd(X0,X0))),rd(X0,X0)))),
inference(forward_demodulation,[status(thm)],[f1334,f18065]) ).
fof(f18067,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,rd(X0,X0))) = mult(rd(X0,X0),mult(ld(rd(X0,X0),X1),mult(rd(X0,X0),rd(X0,X0)))),
inference(forward_demodulation,[status(thm)],[f16791,f18066]) ).
fof(f18068,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,rd(X0,X0))) = mult(mult(X1,rd(X0,X0)),rd(X0,X0)),
inference(forward_demodulation,[status(thm)],[f22,f18067]) ).
fof(f18070,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,rd(X0,X0))) = mult(X0,mult(ld(X0,X1),rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f9473,f18068]) ).
fof(f18115,plain,
! [X0,X1] : mult(X0,mult(ld(X0,X1),rd(X0,X0))) = mult(ld(rd(X0,X0),rd(X0,X0)),mult(X1,rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f18070,f17942]) ).
fof(f18116,plain,
! [X0,X1] : mult(X0,mult(ld(X0,X1),rd(X0,X0))) = mult(rd(rd(X0,X0),rd(X0,X0)),mult(X1,rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f8586,f18115]) ).
fof(f18117,plain,
! [X0,X1] : mult(X0,mult(ld(X0,X1),rd(X0,X0))) = mult(X0,mult(ld(X0,ld(rd(X0,X0),X1)),rd(X0,X0))),
inference(backward_demodulation,[status(thm)],[f18125,f9450]) ).
fof(f18125,plain,
! [X0,X1] : mult(X0,mult(ld(X0,X1),rd(X0,X0))) = mult(rd(X0,X0),mult(X1,rd(X0,X0))),
inference(forward_demodulation,[status(thm)],[f9387,f18116]) ).
fof(f18127,plain,
! [X0,X1] : X0 = mult(rd(X1,X1),mult(X0,mult(rd(X1,X1),rd(X1,X1)))),
inference(forward_demodulation,[status(thm)],[f10,f17944]) ).
fof(f18128,plain,
! [X0,X1] : X0 = mult(rd(X1,X1),mult(X0,rd(X1,X1))),
inference(forward_demodulation,[status(thm)],[f8587,f18127]) ).
fof(f18144,plain,
! [X0,X1] : X0 = mult(X1,mult(ld(X1,X0),rd(X1,X1))),
inference(forward_demodulation,[status(thm)],[f18125,f18128]) ).
fof(f18435,plain,
! [X0,X1] : mult(X0,mult(ld(X0,X1),rd(X0,X0))) = mult(ld(rd(X0,X0),X1),rd(X0,X0)),
inference(forward_demodulation,[status(thm)],[f18070,f18035]) ).
fof(f18436,plain,
! [X0,X1] : X0 = mult(ld(rd(X1,X1),X0),rd(X1,X1)),
inference(forward_demodulation,[status(thm)],[f18144,f18435]) ).
fof(f18437,plain,
( sK2_skl != sK2_skl
| mult(sK0_skl,rd(sK1_skl,sK1_skl)) != sK0_skl ),
inference(backward_demodulation,[status(thm)],[f18595,f8607]) ).
fof(f18440,plain,
! [X0,X1] : rd(X0,rd(X1,X1)) = mult(X0,rd(X1,X1)),
inference(backward_demodulation,[status(thm)],[f18595,f11981]) ).
fof(f18595,plain,
! [X0,X1] : X0 = mult(rd(X1,X1),X0),
inference(forward_demodulation,[status(thm)],[f11,f18036]) ).
fof(f18606,plain,
! [X0,X1] : X0 = mult(X1,mult(ld(X1,ld(rd(X1,X1),X0)),rd(X1,X1))),
inference(forward_demodulation,[status(thm)],[f18144,f18117]) ).
fof(f18626,plain,
! [X0,X1] : X0 = mult(X0,rd(X1,X1)),
inference(backward_demodulation,[status(thm)],[f18680,f18436]) ).
fof(f18680,plain,
! [X0,X1] : X0 = ld(rd(X1,X1),X0),
inference(forward_demodulation,[status(thm)],[f18144,f18606]) ).
fof(f18933,plain,
mult(sK0_skl,rd(sK1_skl,sK1_skl)) != sK0_skl,
inference(trivial_equality_resolution,[status(thm)],[f18437]) ).
fof(f18934,plain,
rd(sK0_skl,rd(sK1_skl,sK1_skl)) != sK0_skl,
inference(backward_demodulation,[status(thm)],[f18440,f18933]) ).
fof(f19641,plain,
! [X0,X1] : X0 = rd(X0,rd(X1,X1)),
inference(forward_demodulation,[status(thm)],[f18440,f18626]) ).
fof(f19960,plain,
sK0_skl != sK0_skl,
inference(forward_demodulation,[status(thm)],[f19641,f18934]) ).
fof(f19961,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f19960]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:29:55 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 61.11/8.64 % Refutation found
% 61.11/8.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 61.11/8.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 30.64/8.91 % Elapsed time: 8.511641 seconds
% 30.64/8.91 % CPU time: 66.604655 seconds
% 30.64/8.91 % Total memory used: 919.090 MB
% 30.64/8.91 % Net memory used: 915.481 MB
%------------------------------------------------------------------------------